# Conoid

From Encyclopedia of Mathematics

A Catalan surface all straight line generators of which intersect a fixed straight line, called an axis of the conoid. For example, a hyperbolic paraboloid is a conoid with two axes.

The position vector of a conoid is given by

where is a unit vector having the same direction as an axis of the conoid and is some function. For a right conoid , , and then its axis is a line of striction. A right conoid with is a helicoid.

#### Comments

#### References

[a1] | M. Berger, B. Gostiaux, "Géométrie différentielle: variétés, courbes et surfaces" , Presses Univ. France (1987) |

[a2] | M.P. Do Carmo, "Differential geometry of curves and surfaces" , Prentice-Hall (1976) |

**How to Cite This Entry:**

Conoid. I.Kh. Sabitov (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Conoid&oldid=18035

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098